Superboost transitions, refraction memory and super-Lorentz charge algebra

TL;DR

<3-5 sentence high-level summary> The paper extends the infrared structure of general relativity by promoting Diff(S^2) super-Lorentz transformations to a physical symmetry alongside supertranslations, requiring a renormalized phase space to keep charges finite. It derives a closed-form description of Minkowski vacua labeled by supertranslation, superboost, and superrotation data, and demonstrates that impulsive transitions between vacua realize refraction/velocity kick memory and a nonlinear displacement memory. A renormalized symplectic structure is constructed, and finite surface charges are defined that reproduce the leading and subleading soft graviton theorems, with a detailed charge algebra closing under a modified bracket and including a 2-cocycle. The work clarifies the relationship between memory effects, vacuum transitions, and Ward identities, and lays the groundwork for a comprehensive Diff(S^2) BMS phase space despite remaining challenges in fully incorporating all superboost transitions.

Abstract

We derive a closed-form expression of the orbit of Minkowski spacetime under arbitrary Diff$(S^2)$ super-Lorentz transformations and supertranslations. Such vacua are labelled by the superboost, superrotation and supertranslation fields. Impulsive transitions among vacua are related to the refraction memory effect and the displacement memory effect. A phase space is defined whose asymptotic symmetry group consists of arbitrary Diff$(S^2)$ super-Lorentz transformations and supertranslations. It requires a renormalization of the symplectic structure. We show that our final surface charge expressions are consistent with the leading and subleading soft graviton theorems. We contrast the leading BMS triangle structure to the mixed overleading/subleading BMS square structure.

Figures (2)

• Figure 1: Contour for the variational principle.
• Figure 2: The infrared structure of asymptotically flat spacetimes at null infinity.